GEOMETRY OF VARIATIONAL PARTIAL DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F16%3AA1701LHP" target="_blank" >RIV/61988987:17310/16:A1701LHP - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
GEOMETRY OF VARIATIONAL PARTIAL DIFFERENTIAL EQUATIONS AND HAMILTONIAN SYSTEMS
Original language description
This is a survey of Hamiltonian field theory in jet bundles with a particular stress on geometric structures associated with Euler?Lagrange and Hamilton equations. Our approach is based on the concept of Lepage manifold, a fibred manifold endowed with a closed Lepage (n + 1)-form where n is the dimension of the base manifold, which serves as a background for formulation of a covariant Hamilton field theory related to an Euler?Lagrange form (representing variational equations), hence to the class of equivalent Lagrangians. Compared with conventional approaches, dependent upon choice of a particular Lagrangian, this is an important distinction which enables us to enlarge substantially the family of field Lagrangians which possess a canonical multisymplectic Hamiltonian formulation on the affine dual of the jet bundle, and can thus be treated without using the Dirac constraint formalism. Within the Hamiltonian theory on Lepage manifolds, the concepts of regularity and Legendre transformation are revisited and extended, and new formulas for the Hamiltonian and momenta are obtained. In this paper we focus on De Donder?Hamilton equations which arise from ?short? (at most 2-contact) Lepage (n + 1)-forms. To illustrate the results we present regular Lepage manifolds (and the corresponding Hamiltonian formulation) for the Einstein and Maxwell equations.4
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-02476S" target="_blank" >GA14-02476S: Variations, geometry and physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Banach Center Publications
ISBN
978-83-86806-34-8
ISSN
0137-6934
e-ISSN
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Number of pages
19
Pages from-to
219-237
Publisher name
Polish Academy of Sciences, Institute of Mathematics
Place of publication
Bedlewo
Event location
Bedlewo
Event date
May 10, 2015
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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